Abstract
Abstract Some properties of many-channel scattering wave functions, of the eigenstates of R-matrix theory and of the R-matrix expansion are studied in the frame of an exactly soluble model. The dependence of the scattering wave function upon energy and entrance channel is investigated both formally and numerically. It is shown that only the closed channel components of the scattering wave function become approximately independent of the entrance channel near resonance. The relation between the actual scattering wave function near resonance and the Gamow state of the Humblet-Rosenfeld theory is discussed. The exact eigenvalues, eigenstates and reduced widths of R-matrix theory are constructed and their dependence upon the choice of boundary parameters is studied. The elements of the R-matrix are computed and the convergence of the level expansion is investigated. The validity of various one-level approximations is analysed. The effect of a direct transition on the width of compound nuclear resonances is exhibited.
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